Complex geometry is defined as the study of complex algebraic geometry and complex analytic geometry, which involve the study of geometric objects and spaces using the tools of complex analysis. Synonyms for "complex geometry" include "algebraic geometry," which focuses on the study of algebraic varieties, or sets of solutions to algebraic equations, and "projective geometry," which studies geometric properties that are invariant under projective transformations. Other related terms include "differential geometry," which studies the geometry of curves and surfaces using differential calculus, and "analytic geometry," which studies the conversion of algebraic equations into geometric representations. Ultimately, all of these terms refer to the study of geometrical structures using algebraic and analytical methods.